Identification of Parameters in a System of Differential Equations Modeling Evolution of Infectious Diseases

The objective of this project was to perform an inverse parameter identification study to determine parameter values in a system of ten ordinary differential equations modeling the prediction of the evolutionary spread of syphilis. The goal was to predict infant mortality rates due to syphilis by using this model and match them to actual field data collected in the United States from 1900 to 1970. The syphilis model was developed by the UCLA Disease Modeling Group. The model involves 23 unknown user-specified parameters, each with specified maximum and minimum possible values. An accurate ordinary differential equation system integration algorithm was used to numerically integrate these equations. A hybrid evolutionary optimization algorithm was then used to iteratively find the proper values of the 23 unknown parameters by minimizing the difference between the predicted and the actual values of annual infant mortality rates due to syphilis. The parameters were originally treated as constants, meaning that they did not vary in time. During this study, they were also considered as time-dependent by modeling them as second degree polynomials. The sexually active population in the original model was assumed linearly increasing with time. To improve on the results, an eight term Fourier series fit was performed on the actual evolution of the sexually active population data during period 1900–1970. It was found that treating the 23 parameters as constants yielded an average fit of the infant mortality rates. By treating the parameters as time-dependent the fit still appeared average, but the variations of mortality during certain periods were captured more accurately.